In general, cranes are one of the most heavily used instruments in construction base sites. There are more than 125,000 cranes operating in the construction industry in United States. Because so many construction activities rely on cranes for moving structural and nonstructural components, the efficiency of the crane operation can influence the entire project progress. However it is always challenging to maintain efficiency of crane operations and the safety of the site. This is especially true in high-rise construction where cranes play a particularly critical role in the overall construction schedule. The challenge for crane operation is the trade-off between the speed/efficiency and the safety.
Cranes are often in charge of the tasks in the critical path of construction schedule. The speed of crane erections can significantly influence the overall project progress. A fast crane operation may result in large sway of the hanging object and causes the safety concerns in the high-speed operation. Accordingly, novice operators usually slow down the crane motions to reduce the sway to ensure the safety of the operation. Although this seems reasonable, the accumulation of hundreds or even thousands slower erection cycles may influence the overall project productivity significantly. Experienced crane operators usually develop the skill and intuition of the crane control for increasing the efficiency and safety of the crane operation. They often vary the speed of the rotation to control the overall vibration in the erection cycle.
There is a prior velocity control method for preventing oscillations in crane, as disclosed in U.S. Pat. No. 5,550,733 (called Case A hereafter), issued on Aug. 27, 1996. Case A applies a closed circuit during the carrying for feeding back the oscillations of the object so as to quickly damping them. The tower crane is a large-scale machine operated at outdoor construction environment. The closed circuit is a close-loop control system which is suitable for use of a small scale machine, but it is difficult to use with the tower crane motor for controlling the suggested precise moving to and fro. Accordingly, an open-loop control system is more suitable for use of the tower crane.
First Referring to FIG. 1, there is shown an ideal model of a tower crane suspended system. The model is a 2D in-plane version of the 3D simulations. The figure illustrates a rigging system that is the hanging system of the tower crane. The crane has a jib 10, a trolley 11, a hook block 12 and a hook 13. Rigging a beam element 14 in the plane perpendicular to crane jib 10 is shown in FIG. 1. There are steel cables 15, 16 under trolley 11. Cables 15, 16 are of low damping and difficult to cease the oscillation. Referring to FIG. 2, an idealized double pendulum model for the tower crane can be found. The model uses a first frictionless pin 20, a first mass-less rigid bar 21, a first rigid connection 22 with a mass m1, a second frictionless pin 23, a second mass-less rigid bar 24, a second rigid connection 25 with a mass m2 and the mass m2 is a rigid object 26. The double pendulum model can more realistically simulate the behavior of the hanging system, for example, including hanging object 14, hook 13 and cables 15, 16, of the crane.
Referring to FIG. 3, the free body diagram of the double pendulum under operation is shown. The double pendulum are with two mass-less rigid bars, the important parameters are L1, L2, m1, and m2, the pendulum length and the suspended mass respectively. The free body diagram depicts the pendulum under external force on the pivot, i.e. pin 23. The arrows indicate the static force directions to the right and to the bottom of the diagram when the pivot acceleration is to the left. The double pendulum equations are as follows:
                                                                        [                                                                                                                              (                                                                                    m                              1                                                        +                                                          m                              2                                                                                )                                                ⁢                                                  L                          1                          2                                                                                                                                                              m                          2                                                ⁢                                                  L                          1                                                ⁢                                                  L                          2                                                                                                                                                                                                  m                          2                                                ⁢                                                  L                          1                                                ⁢                                                  L                          2                                                                                                                                                              I                          G                                                +                                                                              m                            2                                                    ⁢                                                      L                            2                            2                                                                                                                                              ]                            ⁢                              {                                                                                                                              θ                          ¨                                                1                                                                                                                                                                          θ                          ¨                                                2                                                                                            }                                      +                                          [                                                                                                                              (                                                                                    m                              1                                                        +                                                          m                              2                                                                                )                                                ⁢                                                  gL                          1                                                                                                            0                                                                                                  0                                                                                                                m                          2                                                ⁢                                                  gL                          2                                                                                                                    ]                            ⁢                              {                                                                                                    θ                        1                                                                                                                                                θ                        2                                                                                            }                                              =                      {                                                                                                      (                                                                        P                          1                                                +                                                  P                          2                                                                    )                                        ⁢                                          L                      1                                                                                                                                                              P                      2                                        ⁢                                          L                      2                                                                                            }                          ,                            (        1        )            where θ1, θ2 are the rotation angles of double pendulum, {umlaut over (θ)}1, {umlaut over (θ)}2 the angular acceleration, P1, P2 the external forces acting on mass m1, m2. There is almost no control mechanism for the fast crane in the prior art. The acceleration input by the moving motor of the crane should be controlled.
Therefore, how to solve the problems of the oscillation of the steel cable for the crane are solved in the present invention. The inventors endeavor in the experiments, tests and researches to obtain a fast crane and an operation method for the same, which not only resolves the drawback of the oscillation of the hanging object, but also achieves the convenience that the moving time of the hanging object is shortened. Namely, the subject matters to be resolved in the present invention are how to overcome the problem that the sway angle is too large for the hanging object, and consequently the shortening of the moving time of the hanging object is feasible, how to overcome the problem that there is no acceleration between the first and the second accelerations, and how to overcome the problem that the time for the second accelerations is relative to the desired operation maximum speed. The present disclosure aims to develop a simple control method for the fast crane operations. The sway angle should be limited to maintain the controllability and safety. A fast crane based on the prior double pendulum equations will be established according to the embodiments of the present disclosure.